WEBVTT physics/ap-physics-1-2/fullerton
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Hi everyone and welcome back to Educator.com.
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In this mini-lesson we are going to do page 1 of APlusPhysics worksheet on circuit analysis, so with that you will find the link down below.
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We will dive right in.
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Number 1 -- A 30 ohm resistor, a 3 ohm resistor, and an unknown resistor (r) and two ammeters (A1) and (A2) are connected as shown with a 12 volt source and ammeter (A2) reads a current of 5 A.
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Determine the equivalent resistance of the circuit.
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Well, the way I am going to solve something like this is I am going to go through and I am going to make a VIRP table.
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What I am going to do is I am going to name my resistors, so let us call that (R1) and that (R2).
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The elements of my circuits are (R1), (R2), and we will have a row here for total, have a voltage, a current, a resistance, and a power.
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I do not think I am going to need the power in this one, but we will write it in there, just in case.
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And we will fill in what we already know about the circuit.
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We know (R1) is 3 ohms, we know our total potential difference is 12 volts, and we know the current through the entire circuit is 5 A.
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We can figure out once we know two things in any row, we can figure out the others, so resistance is going to be V/I or 12/5, which is going to be 2.4.
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Since this is a parallel circuit, we are going to have the same potential drop across both resistors, so we can fill that in -- 12 and 12 -- and current is I = V/R, so this will be 4 A.
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If we have 4 A going through (R1) -- well if we had 5 A here, we have 4 A going through (R1), we must have 1 A going through (R2).
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Now I can figure out that resistance of our unknown resistor, R = V/I or 12 ohms; so determine the equivalent resistance of the circuit.
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The equivalent resistance of the circuit we already found out was 2.4 ohms.
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Now, as we do this, we are going to answer the next couple of questions using that same table.
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Number 2 -- Calculate the current measured by ammeter (A1).
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Well, the current through (A1) we said was going to be 4 A, right from our VIRP table already, so 4 A.
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Number 3 -- Calculate the resistance of the unknown resistor, also right from out table and that was 12 ohms.
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Moving on to question 4 -- A 9 volt battery is connected to a 4 ohm resistor and a 5 ohm resistor as shown in the diagram.
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What is the current through the 5 ohm resistor?
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Well, I could do this with a VIRP table, but I can probably do this one much more simply because the current is just going to be total voltage over total resistance and this is easy to determine because it gives me both resistors and they are in series.
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So that will be 9 volts/4 ohms + 5 ohms or 9 ohms or just 1 A so the correct answer there is Number 1.
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Number 5 -- An 18 ohm resistor and a 36 ohm resistor are connected in parallel with a 24 volt battery.
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A single ammeter is placed in the circuit to read its total current.
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Draw a diagram of the circuit.
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For our diagram, we have a 24 volt battery and then we have a 18 ohm resistor and it is connected in parallel with that 36 ohm resistor.
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So that is 18 ohms, that one is 36 ohms, which we will call (R1) and (R2).
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Draw the diagram of the circuit -- Done.
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Well now that we have it here, let us go ahead and complete the VIRP table.
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(R1) and (R2) are our elements and a row here for total and we will fill in V-I-R-P.
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Now let us put in what values we happen to know already.
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Our total voltage is 24 volts, (R1) is 18 ohms, and (R2) is 36 ohms.
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As I look at this, because it is a parallel circuit, it is easy to see that the voltage drop across (R1) and (R2) is also 24 volts, so I can fill those in and current then is going to be V/R or 24/18, which is going to be 4/3 or 1.33 amps.
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The current through our two, I = V/R or 24/36 is 2/3 or we will round that off to 0.67 amps and that means that our total current -- if we have through (R1) we have 1.33 amps and through (R2) we have 0.67 amps -- those must come together to give us 2 amps as our total current.
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We can figure out now our total resistance, R = V/I, which will be 12 ohms, which makes sense.
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Our equivalent resistor should be less than any single resistor.
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While we are here, we could calculate the powers too.
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Power equals V × I or 24 × 4/3 = 32 W and 24 × 2/3 = 16 W and 24 × 2 = 48 W or we could have just added up the powers through each resistor.
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Now that we have this VIRP table, we can answer any of the other questions that are going to come up.
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For example, as we go through the next one -- calculate the equivalent resistance of the circuit.
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We just did that and the equivalent resistance was 12 ohms.
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Calculate the total power dissipated in the circuit. Our total power dissipated was 48 W.
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As we do these then, there is our 48 W, so...
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...we have answered all seven questions on the worksheet.
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If you struggled with any of these, now would be a great time to go back and review the video lesson on circuit analysis and VIRP tables or if they went great -- Terrific -- time to move on, keep moving forward.
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Thanks so much for your time everyone and make it a great day!